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I was reading the Wikipedia pages on the graph automorphism, but I could not find any solution to the problem (Not even a brute force one). So, is it indeed true that no solutions exist for the general case of the automorphism problem?

P.S. Are there any significant uses of a solution to this problem in pure mathematics, or is the significance of such a solution mostly practical?

Thank you in advance.

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    $\begingroup$ There's an obvious brute force solution for finite graphs. Are you talking about infinite graphs? $\endgroup$
    – Jim Conant
    Commented Dec 29, 2018 at 17:54
  • $\begingroup$ Yes indeed. Is there currently any way to solve the graph automorphism problem in general for infinite graphs? $\endgroup$
    – J.M.W Turner
    Commented Dec 30, 2018 at 4:22

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It's not even possible to describe all infinite graphs. The only hope is to restrict to a computable subset. In that case it depends heavily on the subset.

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